By Ouissal Moumou
Defying both the prevailing milieu and familial expectations, Sophie Germain opted for the pursuit of mathematics, eschewing the conventional roles prescribed for women during her era. While her pivotal contributions to mathematics, particularly in the fields of number theory and mathematical physics, stand as a testament to her intellectual prowess, regrettably, insufficient credit is given to her contributions, a circumstance attributable, in part, to her gender.
Sophie Germain was born in Paris on April 1, 1776, to an upper-middle-class family. Sophie’s interest in mathematics emerged when she was 13 years old. It was the time of the French Revolution, causing her to stay confined at home due to the danger of the revolts. Consequently, she started spending a lot of time in her father’s library and eventually became intrigued by mathematics. Unfortunately for Sophie, her parents did not like her new interest; they deemed it inappropriate for a woman, a common belief among the middle class at the time. This made her study at night, but it wasn’t long before her parents found out and began to deny her light and heat in the middle of the night. Sophie did not give up, using quilts to keep warm and candles that she would hide. Sophie’s parents eventually gave up and let her pursue her interest in mathematics.
Young Sophie Germain, https://en.wikipedia.org/wiki/Sophie_Germain
When Sophie was 18, she could not attend the newly opened Ecole Polytechnique in Paris because she was a woman. This did not stop her from obtaining lecture notes from an acquaintance and learning from the courses that were offered there. Interested in the work of Lagrange, Sophie decided to send him a paper on analysis for review, under the pseudonym M. LeBlanc, who was a previous student of Lagrange. Impressed by her work, Lagrange became her first mentor, which allowed her to mingle with other scientists and big names in the field.
The M. LeBlanc pseudonym was not restricted to her correspondence with Lagrange, but also with Carl Friedrich Gauss. Interested in his work in number theory, Sophie started sending him some of her work in the same area. She also had correspondence with Legendre to whom she sent what would later become one of her most prominent contributions to number theory which was proving that if x, y, and z are integers and if x5 + y5 = z5, then either x, y, or z must be divisible by 5. After Sophie revealed her identity to Gauss in 1807, his response in one of his letters had the following:
“But when a woman, because of her sex, our customs and prejudices, encounters infinitely more obstacles than men, in familiarizing herself with their knotty problems, yet overcomes these fetters and penetrates that which is most hidden, she doubtless has the most noble courage, extraordinary talent, and superior genius.”
Sophie Germain, https://mathwomen.agnesscott.org/women/germain.htm
Number theory was not the only field that Sophie Germain contributed to. She also contributed to the theory of elasticity. In 1811, Sophie submitted the only entry to France’s Academy of Sciences’ ‘Academy Contest’ in physics and the theory of elasticity. She submitted an anonymous paper but was not selected due to the lack of formalism in her work. After getting her work corrected by Lagrange, she submitted a second time after the contest was extended and earned an honorable mention. In 1816, she submitted a paper with her real name Memoir on the Vibrations of Elastic Plates for the same contest and won the prize. This laid out the ground for her work in the theory of elasticity, and she continued working on it after her win, leading to more papers in the field.
While Sophie published her work on elasticity with the Academy, she did not publish her work on number theory. One could conjecture that her decision was impacted by her experience with the academy, which she encountered after arguing with them about publishing her elasticity research, which she ultimately chose to publish on her dime. Her only published number theory work was a brief article on number theory in the recently established private journal, Journal f̈ur die Reine und Angewandte Mathematik, before her death. Moreover, her only published credited work on Fermat’s Last Theorem was part of Legendre’s work on proving the theorem for n = 5, which appeared in the Memoir of the Royal Academy of Sciences of the Institut de France, in 1827 as a footnote in his work, which is now known as “Sophie Germain’s Theorem”.
Sophie Germain Street in Paris, https://mathwomen.agnesscott.org/women/germain.htm
Before she could receive the honorary degree from the University of Gottingen that Gauss persuaded the institution to award her, Germain passed away in 1831 from breast cancer. If there were to be a theme in Sophie’s life, it would be perseverance and hard work. Despite societal impediments and a lack of formal training, she emerged as a great mathematician, leaving an indelible mark on number theory and the theory of elasticity.
Further Reading
Gray, Mary W. “Sophie Germain,” in Women of Mathematics, A Biobibliographic Sourcebook, Louise S. Grinstein and Paul J. Campbell, editors, Greenwood Press, 1987.
This article contains an excellent bibliography of works written about Sophie Germain.
— “Sophie Germain, A Bicentennial Appreciation,” AWM Newsletter, Vol. 6, No. 6 (1976), 10-14. [Reprint in Complexities: Women in Mathematics, Bettye Anne Case and Anne Leggett, Editors, Princeton University Press (2005), 68-74.]
Bluestocking Oxford 